[LeetCode 4.18] Minimum Path Sum

Minimum Path Sum

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

Example:

Input:
[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.

Python3 Solution:

思路：
计算出到达每个位置的最小路径和(=左边和上边中较小者+当前位置的值)，注意边界和计算顺序（从左到右，从上到下）

class Solution:
    def minPathSum(self, grid: List[List[int]]) -> int:
        m = len(grid)
        if m == 0:
            return 0
        n = len(grid[0])
        if n == 0:
            return 0
        memo = [[0]*n for _ in range(m)]
        memo[0][0] = grid[0][0]
        for j in range(1,n):
            memo[0][j] = memo[0][j-1] + grid[0][j]
        for i in range(1,m):
            memo[i][0] = memo[i-1][0] + grid[i][0]
        for i in range(1,m):
            for j in range(1,n):
                memo[i][j] = min(memo[i][j-1], memo[i-1][j]) + grid[i][j]
        return memo[-1][-1]